The equivalent representations for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment aμHVP in the presence of the quark flavour thresholds are studied. Specifically, the explicit relations between the contributions given by the integration over a finite kinematic interval to aμHVP expressed in terms of the hadronic vacuum polarization function, Adler function, and the R-ratio of electron–positron annihilation into hadrons are derived. It is shown that the quark flavour thresholds of the hadronic vacuum polarization function generate additional contributions to aμHVP expressed in terms of the Adler function and the R-ratio and the explicit expressions for such contributions are obtained. The commonly employed dispersion relations, which bind together hadronic vacuum polarization function, Adler function, and R-ratio, are extended to account for the effects due to the quark flavour thresholds. The examined additional contributions due to the heavy quark thresholds to aμHVP expressed in terms of the R-ratio appear to be quite sizable, that can be of a particular relevance for the data-driven method of assessment of the hadronic part of the muon anomalous magnetic moment.

中文翻译：

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强子真空极化中夸克风味阈值对μ子反常磁矩的贡献


研究了在存在夸克风味阈值的情况下强子真空极化对μ子反常磁矩aμHVP贡献的等效表示。具体来说，推导了有限运动学区间积分对以强子真空极化函数、阿德勒函数和正负电子湮没成强子的R比表示的aμHVP的贡献之间的显式关系。结果表明，强子真空极化函数的夸克风味阈值对以阿德勒函数和 R 比表示的 aμHVP 产生额外的贡献，并获得了此类贡献的显式表达式。常用的色散关系将强子真空极化函数、阿德勒函数和 R 比结合在一起，并被扩展以解释夸克风味阈值造成的影响。由于以 R 比表示的 aμHVP 的重夸克阈值所造成的额外贡献似乎相当大，这对于评估 mu 子异常磁强子部分的数据驱动方法具有特别的相关性。片刻。